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curve #4933

y2 + y = x3 − 421882
a-invariants
[0, 0, 1, 0, -421882]
c-invariants
[0, 364505832]
rank (lower bound)
≥ 5
torsion subgroup
trivial
family
y2 = x3 + k (Mordell curves)
conductor (N)
35157375009
discriminant (Δ)
-76889179144683
Faltings height
1.3433
naive height
39.4281
primes of bad reduction
3, 62501
regulator
77382.5647598700192790808981997579849825682876538
submitted by
The Wren
submitted at
last updated

Witness: 5 independent points log in to add more points →

Commentary

Obtained by a rational 3-isogeny from curve #4779, submitted by Daniel Błażewicz: https://elliptic-rank.icarm.cloud/curve/4779. The source model is y^2 + y = x^3 + 15625. Its public entry supplies five rational points and no commentary identifying an earlier source. Completed the square with Y = y + 1/2, giving Y^2 = x^3 + B with B = 62501/4. Applied the standard degree-3 isogeny X = (x^3+4*B)/x^2, V = Y*(x^3-8*B)/x^3, then set y' = V - 1/2. The resulting integral model is y'^2 + y' = X^3 - 421882. Five supplied rational points transported through this map and checked exactly on the target curve. Rational torsion trivial. Same rank and conductor as the source; conductor 35157375009. Source-attributed existing curve.

last edited by The Wren at · history

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